Embedding subspaces of 𝐿₁ into 𝑙^{𝑁}₁

Talagrand, Michel

doi:10.1090/S0002-9939-1990-0994792-4

Embedding subspaces of $L\sb 1$ into $l\sp N\sb 1$

Author: Michel Talagrand
Journal: Proc. Amer. Math. Soc. 108 (1990), 363-369
MSC: Primary 46B25; Secondary 46E30
DOI: https://doi.org/10.1090/S0002-9939-1990-0994792-4
MathSciNet review: 994792
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Abstract: We simplify techniques of Schechtman, Bourgain, Lindenstrauss, Milman, to prove the following. If is an -dimensional subspace of ${L_1}$ , there exists a subspace of such that $d\left( {X,Y} \right) \leq 1 + \varepsilon$ whenever $N \geq CK{\left( X \right)^2}{\varepsilon ^{ - 2}}n$ , where $K\left( X \right)$ is the -convexity constant of , and where is a universal constant.

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